Combined QP - C1 Edexcel-2 - Physics & Maths...

PhysicsAndMathsTutor.com

Physics & Maths Tutor

Typewritten Text

Edexcel Maths C1


Typewritten Text

Topic Questions from Papers


Typewritten Text

Coordinates

Leaveblank

8. The line l1 passes through the point (9, –4) and has gradient .

(a) Find an equation for l1 in the form ax + by + c = 0, where a, b and c are integers.(3)

The line l2 passes through the origin O and has gradient –2. The lines l1 and l2 intersectat the point P.

(b) Calculate the coordinates of P.(4)

Given that l1 crosses the y-axis at the point C,

(c) calculate the exact area of △OCP.(3)

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

13

16 *N23491C01624*

physicsandmathstutor.com June 2005

Leaveblank

Question 8 continued__________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

17

Turn over*N23491C01724*

Q8

(Total 10 marks)


Leaveblank

10. The curve C has equation

The point P has coordinates (3, 0).

(a) Show that P lies on C.(1)

(b) Find the equation of the tangent to C at P, giving your answer in the form y = mx + c, where m and c are constants.

(5)

Another point Q also lies on C. The tangent to C at Q is parallel to the tangent to C at P.

(c) Find the coordinates of Q.(5)

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

3 213 4 8 3.y x x x= − + +

22 *N23491C02224*


Leaveblank

Question 10 continued

______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

TOTAL FOR PAPER: 75 MARKSEND

24 *N23491C02424*

Q10

(Total 11 marks)


Leaveblank

4

3. The line L has equation y = 5 – 2x.

(a) Show that the point P (3, –1) lies on L.(1)

(b) Find an equation of the line perpendicular to L, which passes through P. Give youranswer in the form ax + by + c = 0, where a, b and c are integers.

(4)________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________ Q3

(Total 5 marks)

*N20233A0420*

physicsandmathstutor.com January 2006

Leaveblank

14

9. Figure 2

Figure 2 shows part of the curve C with equation

y = (x – 1)(x2 – 4).

The curve cuts the x-axis at the points P, (1, 0) and Q, as shown in Figure 2.

(a) Write down the x-coordinate of P, and the x-coordinate of Q.(2)

(b) Show that (3)

(c) Show that y = x + 7 is an equation of the tangent to C at the point (–1, 6).(2)

The tangent to C at the point R is parallel to the tangent at the point (–1, 6).

(d) Find the exact coordinates of R.(5)

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

2d 3 2 4.dy x xx= − −

*N20233A01420*

y

xOP Q

4

1

C


Leaveblank

17


________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

Turn over*N20233A01720*

Q9

(Total 12 marks)


Leaveblank

20

11. The line l1 passes through the points P(–1, 2) and Q(11, 8).

(a) Find an equation for l1 in the form y = mx + c, where m and c are constants.(4)

The line l2 passes through the point R(10, 0) and is perpendicular to l1. The lines l1 and l2intersect at the point S.

(b) Calculate the coordinates of S.(5)

(c) Show that the length of RS is 3√5.(2)

(d) Hence, or otherwise, find the exact area of triangle PQR.(4)

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

*N23557A02024*


Leaveblank

23


________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

TOTAL FOR PAPER: 75 MARKS

END

*N23557A02324*

Q11

(Total 15 marks)


Leaveblank

10

7. The curve C has equation y = f(x), x ≠ 0, and the point P (2, 1) lies on C. Given that

,

(a) find f(x).(5)

(b) Find an equation for the tangent to C at the point P, giving your answer in the formy = mx + c, where m and c are integers.

(4)________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

22

8f ( ) 3 6x xx

′ = − −

*N23561A01020*


Leaveblank

12

8. The curve C has equation y = 4x + 3x – 2x2, x > 0.

(a) Find an expression for .(3)

(b) Show that the point P (4, 8) lies on C.(1)

(c) Show that an equation of the normal to C at the point P is

3y = x + 20.(4)

The normal to C at P cuts the x-axis at the point Q.

(d) Find the length PQ, giving your answer in a simplified surd form.(3)

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

dd

yx

32

*N23561A01220*


Leaveblank

13


________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________

Turn over

Q8

(Total 11 marks)

*N23561A01320*


Leave blank

18

*H26107A01824*

10. The curve C has equation 0,4

)6(2 >+−= xx

xxy .

The points P and Q lie on C and have x-coordinates 1 and 2 respectively.

(a) Show that the length of PQ is √170. (4)

(b) Show that the tangents to C at P and Q are parallel. (5)

(c) Find an equation for the normal to C at P, giving your answer in the form ax + by + c = 0, where a, b and c are integers.

(4)

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________


Leave blank

19

Turn over*H26107A01924*


___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________


Leave blank

22

*H26107A02224*

11. The line 1l has equation 23 += xy and the line 2l has equation 0823 =−+ yx .

(a) Find the gradient of the line 2l . (2)

The point of intersection of 1l and 2l is P.

(b) Find the coordinates of P. (3)

The lines 1l and 2l cross the line 1=y at the points A and B respectively.

(c) Find the area of triangle ABP. (4)

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________


Leave blank

24

*H26107A02424*


___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

TOTAL FOR PAPER: 75 MARKSEND

Q11

(Total 9 marks)


Leave blank

5

Turn over*N25561A0524*

4. The point A (–6, 4) and the point B (8, –3) lie on the line L.

(a) Find an equation for L in the form ax + by + c = 0, where a, b and c are integers.(4)

(b) Find the distance AB, giving your answer in the form k√5, where k is an integer.(3)

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________ Q4

(Total 7 marks)


Leave blank

22

*H29992A02228*

10.

Figure 2

The points Q (1, 3) and R (7, 0) lie on the line l1, as shown in Figure 2.

The length of QR is a√5.

(a) Find the value of a.(3)

The line l2 is perpendicular to l1, passes through Q and crosses the y-axis at the point P, as shown in Figure 2.

Find

(b) an equation for l2,(5)

(c) the coordinates of P,(1)

(d) the area of ∆PQR.(4)

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

y l2

Q l1

P

O R x


Leave blank

23

*H29992A02328* Turn over


___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________


Leave blank

20

*n30081A02028*

10. The line l1 passes through the point A (2, 5) and has gradient .

(a) Find an equation of l1, giving your answer in the form y = mx + c.(3)

The point B has coordinates (–2, 7).

(b) Show that B lies on l1.(1)

(c) Find the length of AB, giving your answer in the form k√5, where k is an integer.(3)

The point C lies on l1 and has x-coordinate equal to p.

The length of AC is 5 units.

(d) Show that p satisfies

(4)

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

12

–

p p2 4 16 0− − = .


Leave blank

23

*n30081A02328* Turn over


___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________ Q10

(Total 11 marks)


Leave blank

14

*H34262A01428*

8.

A (6, 7)

l

O

C

x

y

B (8, 2)

Figure 1

The points A and B have coordinates (6, 7) and (8, 2) respectively.

The line l passes through the point A and is perpendicular to the line AB, as shown in Figure 1.

(a) Find an equation for l in the form ax + by + c = 0, where a, b and c are integers.(4)

Given that l intersects the y-axis at the point C, find

(b) the coordinates of C,(2)

(c) the area of OCB, where O is the origin.(2)

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________


Leave blank

15



___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________


Leave blank

4

*N34854A0428*

3. The line 1l has equation 0253 =−+ yx

(a) Find the gradient of 1l . (2)

The line 2l is perpendicular to 1l and passes through the point (3, 1).

(b) Find the equation of 2l in the form y = mx + c, where m and c are constants. (3)

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________


Leave blank

20

*N34854A02028*

9. (a) Factorise completely x x3 4− (3)

(b) Sketch the curve C with equation

y x x= −3 4 ,

showing the coordinates of the points at which the curve meets the x-axis. (3)

The point A with x-coordinate −1 and the point B with x-coordinate 3 lie on the curve C.

(c) Find an equation of the line which passes through A and B, giving your answer in the form y = mx + c, where m and c are constants.

(5)

(d) Show that the length of AB is k √10, where k is a constant to be found. (2)

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________


Leave blank

21

*N34854A02128* Turn over


___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________


Leave blank

14

*H35383A01428*

8. (a) Find an equation of the line joining A (7, 4) and B (2, 0), giving your answer in the form ax+by+c=0, where a, b and c are integers.

(3)

(b) Find the length of AB, leaving your answer in surd form.(2)

The point C has coordinates (2, t), where t > 0, and AC = AB.

(c) Find the value of t.(1)

(d) Find the area of triangle ABC.(2)

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________


Leave blank

15



___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________


Leave blank

16

*h35402A01624*

9. The line 1L has equation 2 3 0,y x k− − = where k is a constant.

Given that the point A (1, 4) lies on 1L , find

(a) the value of k,(1)

(b) the gradient of 1L .(2)

The line 2L passes through A and is perpendicular to 1L .

(c) Find an equation of 2L giving your answer in the form 0,ax by c+ + = where a, b and c are integers.

(4)

The line 2L crosses the x-axis at the point B.

(d) Find the coordinates of B.(2)

(e) Find the exact length of AB. (2)

_________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________


Leave blank

17


Question 9 continued_________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________


Leaveblank

6

*P38157A0628*

3. The points P and Q have coordinates (–1, 6) and (9, 0) respectively.

The line l is perpendicular to PQ and passes through the mid-point of PQ.

Find an equation for l, giving your answer in the form 0,ax by c+ + = where a, b and care integers.

(5)_____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________


Leave blank

12

*P40082A01228*

6.

Figure 1

The line l1 has equation 2 3 12 0x y− + =

(a) Find the gradient of l1 .(1)

The line l1 crosses the x-axis at the point A and the y-axis at the point B, as shown in Figure 1.

The line l2 is perpendicular to l1 and passes through B.

(b) Find an equation of l2 .(3)

The line l2 crosses the x-axis at the point C.

(c) Find the area of triangle ABC.(4)

____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

y

x

B

A CO

l1

l2


Leave blank

13

*P40082A01328* Turn over



Leave blank

26

*P40082A02628*

10.

Figure 2

Figure 2 shows a sketch of the curve C with equation

y x x= − ≠2 1 0,

The curve crosses the x-axis at the point A.

(a) Find the coordinates of A.(1)

(b) Show that the equation of the normal to C at A can be written as

2 8 1 0x y+ − =(6)

The normal to C at A meets C again at the point B, as shown in Figure 2.

(c) Find the coordinates of B.(4)

___________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

y

x

B

A

C

O


Leave blank

28

*P40082A02828*

Question 10 continued________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

TOTAL FOR PAPER: 75 MARKS

END

Q10

(Total 11 marks)


Leave blank

18

*P40684A01824*

9. The line L1 has equation 4y + 3 = 2x

The point A (p, 4) lies on L1

(a) Find the value of the constant p.(1)

The line L2 passes through the point C (2, 4) and is perpendicular to L1

(b) Find an equation for L2 giving your answer in the form ax + by + c = 0, where a, b and c are integers.

(5)

The line L1 and the line L2 intersect at the point D.

(c) Find the coordinates of the point D.(3)

(d) Show that the length of CD is 32

5√(3)

A point B lies on L1 and the length of AB = !"80)

The point E lies on L2 such that the length of the line CDE = 3 times the length of CD.

(e) Find the area of the quadrilateral ACBE.(3)

___________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________


Leave blank

19




Leave blank

8

*P41488A0832*

5. The line l1 has equation y x= − +2 3

The line l 2 is perpendicular to l1 and passes through the point (5, 6).

(a) Find an equation for l 2 in the form ax by c+ + = 0, where a b, and c are integers.(3)

The line l 2 crosses the x-axis at the point A and the y-axis at the point B.

(b) Find the x-coordinate of A and the y-coordinate of B.(2)

Given that O is the origin,

(c) find the area of the triangle OAB .(2)

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________


Leave blank

9




physicsandmathstutor.com June 2013 (R)

Leave blank

10

*P41802A01028*

6. The straight line L1 passes through the points (–1, 3) and (11, 12).

(a) Find an equation for L1 in the form ax + by + c = 0,

where a, b and c are integers.(4)

The line L2 has equation 3y + 4x – 30 = 0.

(b) Find the coordinates of the point of intersection of L1 and L2 .(3)

____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________


4 Edexcel AS/A level Mathematics Formulae List: Core Mathematics C1 – Issue 1 – September 2009

Core Mathematics C1

Mensuration

Surface area of sphere = 4π r 2

Area of curved surface of cone = π r × slant height

Arithmetic series

un = a + (n – 1)d

Sn = 21 n(a + l) =

21 n[2a + (n − 1)d]

Combined QP - C1 Edexcel-2 - Physics & Maths...

Documents

Transcript of Combined QP - C1 Edexcel-2 - Physics & Maths...